Euler’s Identity Calculator

Euler’s identity is one of the most elegant and profound equations in mathematics, often cited as an example of mathematical beauty. It’s given by:

\[ e^{iθ} = \cos(θ) + i\sin(θ) \]

Where:

• \( e \) is Euler's number (approximately 2.718),
• \( i \) is the imaginary unit,
• \( θ \) is an angle in radians.

Historical Background

Euler’s identity is derived from Euler’s formula, which combines exponential functions with trigonometry, bridging the fields of calculus and complex analysis.

Example Calculation

For \( θ = π \) radians:

\[ e^{iπ} + 1 = 0 \]

This famous special case, known as Euler's Identity, demonstrates how the five most important mathematical constants relate.

Usage

The calculator computes the real and imaginary parts of \( e^{iθ} \) for any angle \( θ \) in radians, helping users visualize complex numbers in polar form.